Police said on Monday that they were investigating an incident in which Manchester City footballer Craig Bellamy confronted a fan on the pitch.
Bellamy marched towards the man, who staged a solo pitch invasion, and shoved him in the face before the fan was led away by match stewards at the Manchester derby game.
Neither the fan nor the Wales international have made a complaint to police about the clash which followed Michael Owen's winner in the 4-3 Manchester United win on Sunday.
A Greater Manchester Police spokesman said: "At the end of the derby between Manchester United and Manchester City at Old Trafford, a member of the public ran on to the pitch, and was detained by police and security staff.
"During this time, there was an altercation between the man and a player from Manchester City FC.
"No formal complaint has been made by either party but police are continuing to make inquiries."
Greater Manchester Police will also investigate a coin-throwing attack on City substitute Javier Garrido, who was struck as he headed down the tunnel at half-time.
The missile was launched from the home section of the crowd as Garrido walked alongside the probable intended target, Carlos Tevez, who was jeered throughout by United fans following his transfer from the home team in the summer.
Twelve people were arrested at the ground for a variety of public order offences and a further 10 were arrested in the city.
A total of 51 supporters were ejected from Old Trafford during the match.
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